Scrub the potatoes and depending on their size, either halve or quarter them to make 1-1/2-inch chunks.
Place them in one of the stock pots and cover with cold water. Add a pinch of salt, bring the water to a boil, cover and cook for 5 minutes. Drain and set aside.
Slice the sausage into 3/8-inch thick rounds and scatter in the bottom of the stockpots.
Rinse the mussels under cool running water and trim any "beards" with a sharp knife. Rinse and inspect the clams in the same manner.
Lay out 2 large squares of cheesecloth and divide a combination of mussels and clams between them. Gather up the ends of the cheesecloth and tie to form a loose-fitting "bag."
Lay the "bags" on top of the sausage rounds, then scatter the potatoes on top. Add the corn next, then lay the lobsters on top.
Cover and cook over medium-high heat for 25 to 30 minutes, or until the lobsters turn bright red. Note: It is not necessary to add water.
While the seafood cooks, melt the butter in a small saucepan and keep warm.
To serve, transfer the seafood and corn to a large platter and the sausage and potatoes to a bowl.
Set out the lemon wedges, and pour the butter into individual ramekins for dipping. Enjoy!